Typical of current large-scale biomedical data is the feature of small number of observed samples and the widely observed sample heterogeneity. Identifying differentially expressed genes related to the sample phenotye (e.g., cancer disease development) and predicting sample phenotype based on the gene expressions are some central research questions in the microarray data analysis. Most existing statistical methods have ignored sample heterogeneity and thus loss power. This project proposes to develop novel statistical methods that explicitly address the small sample size and sampe heterogeneity issues, and can be applied very generally. The usefulness of these methods will be shown with the large-scale biomedical data originating from the lung and kidney transplant research projects. The transplant projects aimed to improve the molecular diagnosis and therapy of lung/kidney allograft rejection by identifying molecular biomarkers to predict the allograft rejection for critical early treatment and rapid, noninvasive, and economical testing. The specific aims are 1) Develop novel statistical methods for differential gene expression detection that explicitly model sample heterogeneity. 2) Develop novel statistical methods for classifying high-dimensional biomedical data and incorporating sample heterogeneity. 3) Develop novel statistical methods for jointly analyzing a set of genes (e.g., genes in a pathway). 4) Use the developed models and methods to answer research questions relevant to public health in the lung and kidney transplant projects;and implement and validate the proposed methods in user-friendly and well-documented software, and distribute them to the scientific community at no charge. It is very important to identify new biomarkers of allograft rejection in lung and kidney transplant recipients. The rapid and reliable detection and prediction of rejection in easily obtainable body fluids may allow the rapid advancement of clinical interventional trials. We propose to study novel methods for analyzing the large-scale biomedical data to realize their full potential of molecular diagnosis and prognosis of transplant rejection prediction for critical early treatment.